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Chapter 1Rethinking ThinkingEveryone thinks. But not everyone thinks equally well. For real intellectual feasts we depend on master chefs who have learned to mix and blend and savor an entire range of mental ingredients. It's not that what they do in the kitchen is any different from what we do, they just do it better. We like to suppose master chefs were born that way, yet even the most promising individuals spend years in training. It follows that we, too, can learn the tools of the trade and thereby improve our own mental cooking. This process, however, requires us to rethink what gourmet intellection is all about. And rethinking shifts our educational focus from what to think to how to think in the most productive ways possible. Our tour of mental cookery begins in the kitchen of the mind, where ideas are marinated, stewed, braised, beaten, baked, and whipped into shape. Just as real chefs surprise us by throwing in a pinch of this and a handful of something else, the kitchens of the creative imagination are full of unexpected practices. Great ideas arise in the strangest ways and are blended from the oddest ingredients. What goes into the recipes often bears no resemblance to the finished dish. Sometimes the master mental chef can't even explain how she knows that her dish will be tasty. She just has a gut feeling that this imagined mixture of ingredients will yield a delicious surprise. Gut feelings don't make obvious sense. Consider, for example, the experience of young Barbara McClintock, who would later earn a Nobel Prize in genetics. One day in 1930 she stood with a group of scientists in the cornfields around Cornell University, pondering the results of a genetics experiment. The researchers had expected that half of the corn would produce sterile pollen, but less than a third of it actually had. The difference was significant, and McClintock was so disturbed that she left the cornfield and climbed the hill to her laboratory, where she could sit alone and think. Half an hour later, she "jumped up and ran down to the field. At the top of the field (everyone else was down at the bottom) I shouted, 'Eureka, I have it! I have the answer! I know what this 30 percent sterility is.' " Her colleagues naturally said, "Prove it." Then she found she had no idea how to explain her insight. Many decades later, McClintock said, "When you suddenly see the problem, something happens that you have the answer - before you are able to put it into words. It is all done subconsciously. This has happened many times to me, and I know when to take it seriously. I'm so absolutely sure. I don't talk about it, I don't have to tell anybody about it, I'm just sure this is it." This feeling of knowing without being able to say how one knows is common. The French philosopher and mathematician Blaise Pascal is famous for his aphorism "The heart has its reasons that reason cannot know." The great nineteenth-century mathematician Carl Friedrich Gauss admitted that intuition often led him to ideas he could not immediately prove. "I have had my results for a long time; but I do not yet know how I am to arrive at them." Claude Bernard, the founder of modern physiology, wrote that everything purposeful in scientific thinking began with feeling. "Feeling alone," he wrote, "guides the mind." Painter Pablo Picasso confessed to a friend, "I don't know in advance what I am going to put on canvas any more than I decide beforehand what colors I am going to use. . . . Each time I undertake to paint a picture I have a sensation of leaping into space. I never know whether I shall fall on my feet. It is only later that I begin to estimate more exactly the effect of my work." Composer Igor Stravinsky also found that imaginative activity began with some inexplicable appetite, some "intuitive grasp of an unknown entity already possessed but not yet intelligible." The Latin American novelist Isabel Allende has described a similarly vague sense propelling her work: "Somehow inside me - I can say this after having written five books - I know that I know where I am going. I know that I know the end of the book even though I don't know it. It's so difficult to explain." Knowing in such ambiguous, inarticulate ways raises an important question. McClintock put it this way: "It had all been done fast. The answer came, and I'd run. Now I worked it out step by step - it was an intricate series of steps - and I came out with what it was. . . . It worked out exactly as I'd diagrammed it. Now, why did I know, without having done a thing on paper? Why was I so sure that I could tell them with such excitement and just say, 'Eureka, I solved it'?" McClintock's query strikes at the heart of understanding creative thinking, as do the experiences of Picasso and Gauss, of composers and physiologists. Where do sudden illuminations or insights come from? How can we know things that we cannot yet say, draw, or write? How do gut feelings and intuitions function in imaginative thinking? How do we translate from feeling to word, emotion to number? Lastly, can we understand this creative imagination and, understanding it, can we exercise, train, and educate it? Philosophers and psychologists have pondered these and related questions for hundreds of years. Neurobiologists have sought the answers in the structures of the brain and the connections between nerve synapses. Full answers still elude us. But one source of insight into creative thinking has been greatly undervalued and underused: the reports of eminent thinkers, creators, and inventors themselves. Their introspective reports cannot answer all our questions about thinking, but they certainly provide important and surprising new avenues to explore. Above all, they tell us that conventional notions of thinking are at best incomplete, for they leave out nonlogical forms of thinking that can't be verbalized. Take the testimony of physicist Albert Einstein, for instance. Most people would expect Einstein to have described himself as solving his physics problems using mathematical formulas, numbers, complex theories, and logic. In fact, a recent book by Harvard psychologist Howard Gardner, Creating Minds, portrays Einstein as the epitome of the "logico-mathematical mind." His peers, however, knew that Einstein was relatively weak in mathematics, often needing to collaborate with mathematicians to push his work forward. In fact, Einstein wrote to one correspondent, "Do not worry about your difficulties in mathematics. I can assure you that mine are still greater." Einstein's mental strengths were quite different, as he revealed to his colleague Jacques Hadamard. "The words of the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined. . . . The above mentioned elements are, in my case, of visual and some of muscular type." In a kind of thought experiment that could not be articulated, he pretended to be a photon moving at the speed of light, imagining what he saw and how he felt. Then he became a second photon and tried to imagine what he could experience of the first one. As Einstein explained to Max Wertheimer, a psychologist, he only vaguely understood where his visual and muscular thinking would take him. His "feeling of direction," he said, was "very hard to express." McClintock, for her part, talked about developing a "feeling for the organism" quite like Einstein's feeling for a beam of light. She got to know every one of her corn plants so intimately that when she studied their chromosomes, she could truly identify with them: "I found that the more I worked with them the bigger and bigger [they] got, and when I was really working with them I wasn't outside, I was down there. I was part of the system. I even was able to see the internal parts of the chromosomes - actually everything was there. It surprised me because I actually felt as if I were right down there and these were my friends. . . . As you look at these things, they become part of you. And you forget yourself. The main thing about it is you forget yourself." A similar emotional involvement played a critical role in the prelogical scientific thinking of Claude Bernard, who wrote, "Just as in other human activities, feeling releases an act by putting forth the idea which gives a motive to action." For Wolfgang Pauli, a mathematical physicist, emotional response functioned in the place of ideas that had not yet been articulated. Within the "unconscious region of the human soul," he wrote, "the place of clear concepts is taken by images of powerful emotional content, which are not thought, but are seen pictorially, as it were, before the mind's eye." Some scientists insist that thinking in feelings and mental images can be rationally manipulated. Einstein suggested "a certain connection" between "the psychical entities which seem to serve as elements in thought" and "relevant logical concepts." Mathematician Stanislaw Ulam made the argument even more strongly. He experienced abstract mathematical notions in visual terms, so the idea of "'an infinity of spheres or an infinity of sets'" became "a picture with such almost real objects, getting smaller, vanishing on some horizon." Such thinking is "not in terms of words or syllogisms or signs" but in terms of some "visual algorithm" having a "sort of meta- or super-logic with its own rules." For William Lipscomb, a Nobel laureate in chemistry and, not incidentally, a fine musician, this kind of thinking is a synthetic and aesthetic experience. In his research into the chemistry of boron he found himself thinking not only inductively and deductively but also intuitively. "I felt a focusing of intellect and emotions which was surely an aesthetic response," he wrote. "It was followed by a flood of predictions coming from my mind as if I were a bystander watching it happen. Only later was I able to begin to formulate a systematic theory of structure, bonding and reactions for these unusual molecules. . . . Was it science? Our later tests showed it was. But the processes that I used and the responses that I felt were more like those of an artist." Gut feelings, emotions, and imaginative images do make sense in science, but, like the meaning of a dance or a musical theme, that sense is felt rather than defined. "Intuition or mathematics?" asks inventor and science fiction writer Arthur C. Clarke. "Do we use models to help us find the truth? Or do we know the truth first, and then develop the mathematics to explain it?" There is no doubt about the answer: gut feelings and intuitions, an "essential feature in productive thought," as Einstein put it, occur well before their meaning can be expressed in words or numbers. In his own work, mathematics and formal logic were secondary steps: "Conventional words or other signs [presumably mathematical ones] have to be sought for laboriously only in a secondary stage, when the associative play already referred to is sufficiently established and can be reproduced at will." To Wertheimer he explained, "No really productive man thinks in such a paper fashion. The way the two triple sets of axioms are contrasted in [Einstein's physics book with collaborator Leopold Infeld] is not at all the way things happened in the process of actual thinking. This was merely a later formulation of the subject matter, just a question of how the thing could best be written . . . but in this process they [the ideas] did not grow out of any manipulation of axioms." As he told Infeld, "No scientist thinks in formulae." Scientists may not think in mathematical terms, but the need to express intuitive insight in a form comprehensible to others compels them, in McClintock's words, to "work with so-called scientific methods to put it into their frame after you know." Other scientists confirm the two-part process of intuitive, imaginative understanding followed, necessarily, by logical expression. Metallurgist Cyril Stanley Smith of the Massachusetts Institute of Technology (MIT) has said, "The stage of discovery was entirely sensual and mathematics was only necessary to be able to communicate with other people." Werner Heisenberg, who formulated the uncertainty principle, wrote that "mathematics . . . played only a subordinate, secondary role" in the revolution in physics he helped to create. "Mathematics is the form in which we express our understanding of nature; but it is not the content of that understanding." Nobel Prize-winning physicist Richard Feynman, who also saw and felt things intuitively, noted, "In certain problems that I have done, it was necessary to continue the development of the picture as the method, before the mathematics could really be done." So much for the myth that scientists think more logically than others. To think creatively is first to feel. The desire to understand must be whipped together with sensual and emotional feelings and blended with intellect to yield imaginative insight. Indeed, the intimate connections between thinking, emotions, and feelings are the subject of a startling book called Descartes' Error (1994), which revisits the famous philosopher's separation of mind (and thinking) from body (and being or feeling) more than three hundred years ago. The author, neurologist Antonio Damasio, finds that neurological patients whose emotional affect is grossly altered due to strokes, accidents, or tumors lose the ability to make rational plans. Because they are unable to become emotionally involved in their decisions, they fail to make good ones. Our feelings - our intuitions - are not impediments to rational thinking, they form its origin and bases. For Damasio, body and mind, emotion and intellect are inseparable. We agree. Not only do scientists feel their way toward logical ideas, but creative thinking and expression in every discipline are born of intuition and emotion. For many people this may come as something of a surprise.